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RIGIDITY OF GRADIENT RICCI SOLITONS
We define a gradient Ricci soliton to be rigid if it is a flat bundle N ×GRk where N is Einstein. It is known that not all gradient solitons are rigid. Here we offer several natural conditions on theExpand
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On the classification of gradient Ricci solitons
We show that the only shrinking gradient solitons with vanishing Weyl tensor and Ricci tensor satisfying a weak integral condition are quotients of the standard ones S n , S n 1 R and R n . ThisExpand
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COMPARISON GEOMETRY FOR THE BAKRY-EMERY
For Riemannian manifolds with a measure (M, g, e f dvolg) we prove mean curvature and volume comparison results when the ∞Bakry-Emery Ricci tensor is bounded from below and f or |∇f | is bounded,Expand
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A warped product version of the Cheeger-Gromoll splitting theorem
We prove a new generalization of the Cheeger-Gromoll splitting theorem where we obtain a warped product splitting under the existence of a line. The curvature condition in our splitting is aExpand
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On the classification of warped product Einstein metrics
The question of when an Einstein metric can be written as a warped product is posed in the text Einstein metrics by Besse. Recently, there have been some interesting results about these spaces foundExpand
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On Gradient Ricci Solitons with Symmetry
We study gradient Ricci solitons with maximal symmetry. First we show that there are no nontrivial homogeneous gradient Ricci solitons. Thus, the most symmetry one can expect is an isometricExpand
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On the geometry of Riemannian manifolds with density
We introduce a new geometric approach to a manifold equipped with a smooth density function that takes a torsion-free affine connection, as opposed to a weighted measure or Laplacian, as theExpand
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Stochastic principles governing alternative splicing of RNA
TLDR
The dominance of the major transcript isoform relative to other isoforms from the same gene generated by alternative splicing (AS) is essential to the maintenance of normal cellular physiology. Expand
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Gradient shrinking Ricci solitons of half harmonic Weyl curvature
Gradient Ricci solitons and metrics with half harmonic Weyl curvature are two natural generalizations of Einstein metrics on four-manifolds. In this paper we prove that if a metric has structures ofExpand
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Positive weighted sectional curvature
In this paper, we give a new generalization of positive sectional curvature called positive weighted sectional curvature. It depends on a choice of Riemannian metric and a smooth vector field. WeExpand
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